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And from hence the Value of a may be found, as in the last Pros blem, due Regard being had to the Signs of every Term.
This Work of reducing, or preparing Æquation, for a Solution by Division, hath always been taught both by ancient and modern Writers of Algebra, as a Work so necessary to be done, that they do not so much as give a Hint at the Solution of any adfected Equation without it.
Now it very often happens, that, in dividing all the Terms of an Æquation, some of their Quotients will not only run into a long Series, but also into imperfect Fractions (as in this Æquation above) which renders the Solution both tedious and imperfe&t.
To remedy that Imperfection, I shall here thew how this Æquation (and consequently any other) may be resolv'd without such Division, or Reduction.
This is plain and easily conceived. The next Thing will be how to estimate the first Value of r; and, to perform that, let G be divided by b, only so far as to determine how many Places of whole Numbers there will be in the Quotient ; consequently, how many Points there must be (according to the Height of the Æquation.)
Thus b = 2018) G J 274183922,25(130000
СНАР. у PraEtical Problems, and Kules for finding the Superficial
Contents, or area's of Right-lin'd Figures. DEfore I proceed to the following Problems, it may be conve:D nient to acquaint the Learner, that the Superficies or Area of any Figure, whether it be Right-lin'd or Circular, is composed or made up of Squares, either greater or less, according to the different Measures by which the Dimensions of the Figure are taken or mea. fur’d.
That is, if the Dimensions are taken in Inches, the Area will be composed of square inches ; if the Dimensions are taken in Feet, che Area will be composed of Square Feet ; if in Yards, the Area will be square Yards ; and if the Dimensions are taken by Poles or Perches, (as in Surveying of Land, &c.) then the Area will be square Perches, &c. These Things being understood, and